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- W2041763669 abstract "Functions of the form w ( z ) F ( z ) with F analytic and w ( z )=1, (z 2 −1) 1 2 , (z + 1) 1 2 or (z−1) 1 2 are approximated in the ellipse ξ r :|z+(z 2 −1) 1 2 |=r by w ( z ) p n ( z ), where p n is a polynomial of degree n . Here p n is obtained by the expansion of F in Chebyshev polynomials of the first, second, third or fourth kinds, corresponding to the above four respective weight functions. Bounds are established and computed for the norms on ξ r of the corresponding projections, thus confirming that all resulting approximations are near-minimax within relative distances asymptotically proportional to 4π −2 ln n , and extending a known result (Geddes, 1978) for w ( z )=1 and first kind Chebyshev polynomials." @default.
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- W2041763669 date "1993-06-01" @default.
- W2041763669 modified "2023-09-26" @default.
- W2041763669 title "Near-minimax complex approximation by four kinds of Chebyshev polynomial expansion" @default.
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- W2041763669 doi "https://doi.org/10.1016/0377-0427(93)90303-s" @default.
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